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Search Results: 1 - 10 of 104519 matches for " Weiping Zhang "
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International Students and U.S. Academic Libraries Revisited
  Weiping Zhang
Journal of Library and Information Science , 2006,
Abstract: 頁次:6-17
Heat kernels and the index theorems on even and odd dimensional manifolds
Weiping Zhang
Mathematics , 2003,
Abstract: In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss the odd dimensional counterparts of the above results. In particular, we describe a joint result with Xianzhe Dai on an index theorem for Toeplitz operators on odd dimensional manifolds with boundary.
Eta invariant and Chern-Simons current
Weiping Zhang
Mathematics , 2003,
Abstract: We show that the R/Z part of the analytically defined eta invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, we discuss the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and prove an R refinement in the case where the Dirac operator is replaced by the Signature operator. We also extend the above discussion to the case of eta invariants associated to Hermitian vector bundles with non-unitary connection, which are constructed by using a trick due to Lott.
Circle actions and Z/k-manifolds
Weiping Zhang
Mathematics , 2003,
Abstract: We establish an S^1-equivariant index theorem for Dirac operators on Z/k-manifolds. As an application, we generalize the Atiyah-Hirzebruch vanishing theorem for S^1-actions on closed spin manifolds to the case of Z/k-manifolds.
Dirac operators on foliations: the Lichnerowicz inequality
Weiping Zhang
Mathematics , 2012,
Abstract: We construct Dirac operators on foliations by applying the Bismut-Lebeau analytic localization technique to the Connes fibration over a foliation. The Laplacian of the resulting Dirac operators has better lower bound than that obtained by using the usual adiabatic limit arguments on the original foliation. As a consequence, we prove an extension of the Lichnerowicz-Hitchin vanishing theorem to the case of foliations.
A note on the Lichnerowicz vanishing theorem for proper actions
Weiping Zhang
Mathematics , 2015,
Abstract: We prove a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions. This extends a previous result of Ziran Liu who proves it for the case where the acting group is unimodular.
Vanishing theorems on foliations
Weiping Zhang
Mathematics , 2015,
Abstract: We prove the following generalization of the Lichnerowicz-Hitchin vanishing theorem to the case of foliations: let $M$ be a closed spin manfold, let $F$ be an integrable subbundle of the tangent bundle $TM$ such that $F$ carries a metric of positive leafwise scalar curvature, then the canonical $KO$-characteristic number $\hat{\mathcal A}(M)$ vanishes. Our proof applies to give a geometric proof of the Connes vanishing theorem, which states that in the case of $F$ being spin instead of $TM$ being spin, one has $\hat{A}(M)=0$.
A mod 2 index theorem for pin$^-$ manifolds
Weiping Zhang
Mathematics , 2015,
Abstract: We establish a mod 2 index theorem for real vector bundles over 8k+2 dimensional compact pin$^-$ manifolds. The analytic index is the reduced $\eta$ invariant of (twisted) Dirac operators and the topological index is defined through $KO$-theory. Our main result extends the mod 2 index theorem of Atiyan and Singer to non-orientable manifolds.
Holomorphic quantization formula in singular reduction
Weiping Zhang
Mathematics , 1998,
Abstract: We show that the holomorphic Morse inequalities proved by Tian and the author [TZ1, 2] are in effect equalities by refining the analytic arguments in [TZ1, 2].
The Mathematical Work of V. K. Patodi
Weiping Zhang
Statistics , 2015,
Abstract: We give a brief survey on aspects of the local index theory as developed from the mathematical works of V. K. Patodi. It is dedicated to the 70th anniversary of Patodi.
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